FP3 - 2 Limits Questions - Stuck
Maths and statistics discussion, revision, exam and homework help.
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FP3 - 2 Limits Questions - StuckReady To Answer Now - Latex Problem Sorted
If I didn't rep you that's because I couldn't
Q1:
I have tried multiplying top and bottom by
and that didn;t get me anywhere, I then tried expanding the ex's and after some working eventually got stuck at
![\displaystyle \dfrac{1+2x+\dfrac{x^2}{2}+...}{-1-\frac{x^2}{2}+\cdots}
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= (-1)(1+2x+\dfrac{x^2}{2} + \cdots)(1+ (\dfrac{x^2}{2} + \dfrac{x^3}{6}+\cdots))^{-1}](http://www.thestudentroom.co.uk/latexrender/pictures/04/04b27943f0fea31e717736f06f97673d.png "\displaystyle \dfrac{1+2x+\dfrac{x^2}{2}+...}{-1-\frac{x^2}{2}+\cdots}
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= (-1)(1+2x+\dfrac{x^2}{2} + \cdots)(1+ (\dfrac{x^2}{2} + \dfrac{x^3}{6}+\cdots))^{-1}")
I have been on it for a while so a solution would be better than a hint, unless there is something small that I am missing or a mistake somewhere.
Q2:
![\displaystyle F(x) = \dfrac{e^x}{1-x}
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\text{Show that} F(x) \to -\infty \ \text {as} \ x \to \infty](http://www.thestudentroom.co.uk/latexrender/pictures/a8/a86d00f7036342171b673624840eec96.png "\displaystyle F(x) = \dfrac{e^x}{1-x}
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\text{Show that} F(x) \to -\infty \ \text {as} \ x \to \infty")
For this one I expanded ex and brought the (1-x) to the top and expanded it, multiplied it out and I am stuck at
Same as above, all help is appreciated.
ThnxLast edited by member910132; 12-05-2012 at 16:42. -
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Re: FP3 - 2 Limits Questions - StuckYea, that works lol. The answer is -1, why didn't I see something so simple !!(Original post by ian.slater)
On Q1 you could try multiplying top and bottom by e^-x. -
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Re: FP3 - 2 Limits Questions - Stucksecond one:(Original post by member910132)
Ready To Answer Now - Latex Problem Sorted
Q1:
I have tried multiplying top and bottom by and that didn;t get me anywhere, I then tried expanding the ex's and after some working eventually got stuck at
I have been on it for a while so a solution would be better than a hint, unless there is something small that I am missing or a mistake somewhere.
Q2:
For this one I expanded ex and brought the (1-x) to the top and expanded it, multiplied it out and I am stuck at
Same as above, all help is appreciated.
Thnx
large +ve x makes e^x +ve and 1-x -ve so F is -ve. Now consider the relative order of exponentials and linear expressions in x. -
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Re: FP3 - 2 Limits Questions - StuckJust tried that for Q2 and I get:(Original post by ian.slater)
On Q1 you could try multiplying top and bottom by e^-x.
Using the general result that xe^(-x) tends to 0 as x tends to infinity my only problem is showing how F(x) goes to negative infinity and not just infinity.
Last edited by member910132; 12-05-2012 at 15:38. -
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Re: FP3 - 2 Limits Questions - StuckYou could use L'Hopital' s Theorem...they both come out very easily then.....(Original post by member910132)
Ready To Answer Now - Latex Problem Sorted
Q1:
I have tried multiplying top and bottom by and that didn;t get me anywhere, I then tried expanding the ex's and after some working eventually got stuck at
I have been on it for a while so a solution would be better than a hint, unless there is something small that I am missing or a mistake somewhere.
Q2:
For this one I expanded ex and brought the (1-x) to the top and expanded it, multiplied it out and I am stuck at
Same as above, all help is appreciated.
Thnx -
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Re: FP3 - 2 Limits Questions - StuckSorry, I don't follow the second part.(Original post by ben-smith)
second one:
large +ve x makes e^x +ve and 1-x -ve so F is -ve. Now consider the relative order of exponentials and linear expressions in x. -
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Re: FP3 - 2 Limits Questions - StuckThat isn't on the AQA FP3 syllabus and I don't want to learn stuff that ain't on the syllabus.(Original post by mikelbird)
You could use L'Hopital' s Theorem...they both come out very easily then..... -
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Re: FP3 - 2 Limits Questions - Stuckfrom an intuitive point of view, e^x is like a polynomial of very high degree and so it's going to tend to infinity faster than a linear function.(Original post by member910132)
Sorry, I don't follow the second part. -
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Re: FP3 - 2 Limits Questions - Stuckx e^-x > e^-x(Original post by member910132)
Just tried that for Q2 and I get:
Using the general result that xe^(-x) tends to 0 as x tends to infinity my only problem is showing how F(x) goes to negative infinity and not just infinity.
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Re: FP3 - 2 Limits Questions - StuckNot allowed.(Original post by mikelbird)
You could use L'Hopital' s Theorem...they both come out very easily then..... -
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Re: FP3 - 2 Limits Questions - StuckI'd be happy with it.(Original post by member910132)
Bump - will anyone verify my above post so I can finish this thread ?
